Phys 198 January 15, 1997
Light is an electomagnetic wave propagating in a direction
perpendicular to the plane defined by the orthogonal electric and
magnetic vectors which constitute the wave. Polarization refers
to the direction of the E field vector. This
direction can either be stationary or changing. If the direction
of the E vector changes randomly, the light is
said to be unpolarized (or sometimes, to be randomly polarized).
If the E vector's direction is stationary, the
light is said to be linearly polarized; if the direction of the
vector rotates uniformly while its magnitude is constant, the
light is said to be circularly polarized (left circularly
polarized if the rotation is clockwise as viewed head-on, right
circularly polarized otherwise). Other types of polarization are
possible, even common (e.g. elliptical polarization), but linear
and circular are the major forms of polarization of interest in
optics.
Most materials have a specific index of refraction n which allows the speed of light through the material to be determined (n = c/v, where c is the speed of light in vacuum, and v is the speed of light through the material). Although the index may vary somewhat with the wavelength of the light involved, the material is generally assigned a single value of the index n. However, some materials, because of molecular symmetries, have different indicies for different directions of polarization of light traveling through the material. For instance, many plastics are called birefringent because when they are produced in flat sheets, light incident normally on the sheet encounters two orthogonally oriented axes with slightly different indicies. Generally, if the plastic is stress-free (perhaps it was annealed), the birefringence or difference between the two indicies is negligible. However, if the material is stressed or subjected to some type of loading which affects atomic spacing and bonding, the birefringence becomes very significant. Indeed, the birefringence is linearly proportional to the stress. When the two indicies differ significantly, the axis with the smaller index value is called the fast axis, and the other is called the slow axis. When a light beam travels normally through these plastics, the output beam consists of two orthogonally polarized components which are out of phase with each other by an amount which depends on the difference between the two indicies and the thickness of the material. If a plastic sheet is prepared such that the phase difference between the two output components is 90 degrees, and normally incident linearly polarized light whose polarization direction bisects the right angle between the fast and the slow axis travels through the sheet, the output beam will consist of two equal components of orthogonally polarized light in quadrature. Such a beam is said to be circularly polarized. Since there are two possible directions in which the incident beam can satisfy the requirement of bisection, the output beam can be circularly polarized so as to rotate clockwise or counterclockwise as viewed head-on. These two circular polarizations are also called right circular and left circular, respectively. A sheet which introduces the requisite 90-degree phase difference is called a quarter-wave plate. Such plates are very important in the study of photoelasticity.
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